TEX twocolumn style in AASTeX63
Direct Detection of Black Hole-Driven Turbulence in the Centers of Galaxy Clusters
Yuan Li,1 Marie-Lou Gendron-Marsolais,2Irina Zhuravleva,3 Siyao Xu,4 Aurora Simionescu,5, 6, 7 Grant R. Tremblay,8 Cassandra Lochhaas,9, 10 Greg L. Bryan,11, 12 Eliot Quataert,1 Norman W. Murray,13, 14
Alessandro Boselli,15 Julie Hlavacek-Larrondo,16Yong Zheng,1Matteo Fossati,17 Miao Li,12 Eric Emsellem,18, 19 Marc Sarzi,20 Lev Arzamasskiy,21 and Ethan T. Vishniac22
1Department of Astronomy, University of California, Berkeley, CA 94720, USA
2European Southern Observatory, Alonso de C´ordova 3107, Vitacura, Casilla 19001, Santiago, Chile 3Department of Astronomy & Astrophysics, University of Chicago, 5640 S Ellis Ave, Chicago, IL 60637, USA
4Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706, USA 5SRON Netherlands Institute for Space Research Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
6Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
7Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa 277-8583, Japan 8Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA
9Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, USA 10Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD 21218, USA
11Department of Astronomy, Columbia University, 550 West 120th Street, New York, NY 10027, USA 12Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA 13Canadian Institute for Theoretical Astrophysics, 60 St George Street, University of Toronto, ON M5S 3H8, Canada
14Canada Research Chair in Astrophysics
15Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France
16D´epartement de Physique, Universit de Montr´eal, Succ. Centre-Ville, Montr´eal, Qu´ebec, H3C 3J7, Canada
17Institute for Computational Cosmology and Centre for Extragalactic Astronomy, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
18European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching, Germany
19Univ Lyon, Univ Lyon1, ENS de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon, UMR5574, F-69230 Saint-Genis-Laval France
20Armagh Observatory and Planetarium, College Hill, Armagh BT61 9DG, Northern Ireland 21Department of Astrophysical Sciences, Princeton University, Ivy Lane, Princeton, NJ 08540
22Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD, USA ABSTRACT
Supermassive black holes (SMBHs) are thought to provide energy that prevents catastrophic cooling in the centers of massive galaxies and galaxy clusters. However, it remains unclear how this “feedback” process operates. We use high-resolution optical data to study the kinematics of multi-phase filamen-tary structures by measuring the velocity structure function (VSF) of the filaments over a wide range of scales in the centers of three nearby galaxy clusters: Perseus, Abell 2597 and Virgo. We find that the motions of the filaments are turbulent in all three clusters studied. There is a clear correlation between features of the VSFs and the sizes of bubbles inflated by SMBH driven jets. Our study demonstrates that SMBHs are the main driver of turbulent gas motions in the centers of galaxy clusters and suggests that this turbulence is an important channel for coupling feedback to the environment. Our measured amplitude of turbulence is in good agreement with Hitomi Doppler line broadening measurement and X-ray surface brightness fluctuation analysis, suggesting that the motion of the cold filaments is well-coupled to that of the hot gas. The smallest scales we probe are comparable to the mean free path in the intracluster medium (ICM). Our direct detection of turbulence on these scales provides the clearest evidence to date that isotropic viscosity is suppressed in the weakly-collisional, magnetized intracluster plasma.
yuan.astro@berkeley.edu
1. INTRODUCTION
Relaxed galaxy clusters often harbor a cool core, where radiative cooling of the ICM is expected to result
in cooling flows of hundreds of M yr−1 in the absence
of heating (Fabian 1994). Feedback from active galac-tic nuclei (AGN) in forms of jets, radiation, and fast outflows is thought to provide the energy to balance ra-diative cooling and suppress star formation (McNamara et al. 2005). X-ray observations show that AGN feed-back generates “bubbles” and “ripples” in the surround-ing intra-cluster medium (ICM) (Fabian 2012). Based on X-ray measurements of line widths (Hitomi Collab-oration et al. 2016) and surface brightness fluctuations (Zhuravleva et al. 2014,2016), it is suggested that clus-ter cores are turbulent. However, current X-ray obser-vatories have limited spatial and spectral resolutions, making it impossible to probe turbulence directly, let alone its drivers.
The centers of cool-core clusters also frequently ex-hibit extended filamentary structures that can be seen in the Hα (Conselice et al. 2001; Olivares et al. 2019) and sometimes CO (Edge 2001;McNamara et al. 2014). The existence of cold filaments has been linked to the activities of SMBHs in the centers of galaxy clusters (Cavagnolo et al. 2008;Tremblay et al. 2016). The fila-ments often show perturbed kinematics and a lack of or-dered motion on large scales (Sarzi et al. 2006; Gendron-Marsolais et al. 2018; Olivares et al. 2019). In other words, the motion of the filaments appears turbulent.
In this work, we study the turbulent nature of multi-phase filaments by measuring their VSFs in three nearby galaxy clusters: Perseus, Abell 2597 and Virgo. We de-scribe the data and data processing in Section 2. In Section 3, we connect the turbulent motions of the fil-aments to the activities of SMBHs, and compare our measurements with the X-ray analysis. In Section4, we discuss the puzzling features of the VSFs, the uncertain-ties of the analysis, and the implications of our results, including constraints on microscopic physics of the ICM. We conclude this work in Section5.
2. DATA PROCESSING
The Perseus Hα filaments were observed using the op-tical imaging Fourier transform spectrometer SITELLE at the Canada France Hawaii Telescope (CFHT) (Gendron-Marsolais et al. 2018). SITELLE has a spatial resolution of 0.32100×0.32100, and a spectral resolution of
R = 1800. The original Perseus data cube was binned up by a factor of 2 to increase the signal-to-noise ra-tio. The ionized filaments in Virgo and Abell 2597 was observed using the Multi Unit Spectroscopic Explorer (MUSE) with a spatial sampling of 0.200 and a spectral resolution of R = 3000 (Sarzi et al. 2018; Boselli et al. 2019;Tremblay et al. 2018). For Perseus and Virgo, the velocity in each pixel of the velocity map is obtained
as the peak of a Gaussian profile fit to the Hα + NII complex, and for Abell 2597, only Hα is used in the fit. In Perseus, a small region in the center with a radius of 600is excluded from the fitting due to contamination from the AGN (Gendron-Marsolais et al. 2018). The molecular gas in Abell 2597 and Virgo was observed us-ing the Atacama Large Millimeter/submillimeter Array (ALMA) with a spatial resolution of 0.3700 (Simionescu et al. 2018; Tremblay et al. 2018). See Table 1 for a summary of data.
To understand the nature of the motion of these fila-ments, we compute the VSFs for all three clusters. We first remove a small fraction (< 20%) of pixels with large velocity errors, shown in the top panels of Figure1. We have visually examined pixels with very large velocity errors, and found that they tend to be located either at the edge of filaments or in isolation with an appearance similar to noise (even though it could be from a real gas cloud that is very faint and poorly resolved). Therefore, it is sensible to remove these pixels. The value of the velocity error cut is chosen to be a few times the median velocity error for each cluster. We have verified that the results are not sensitive to the exact choice of this value. For Perseus, an additional flux cut is applied to remove pixels with low signal-to-noise (Gendron-Marsolais et al. 2018).
For each clean velocity map, we compute the first-order VSF in the following way: for each pair of pixels, we record the projected physical separation ` of the pair and compute the velocity difference δv of the two pixels. The bottom panels of Figure1 show the distribution of `. We then compute the average absolute value of the velocity differences h|δv|i within bins of `. The uncer-tainties in the VSFs are obtained by propagating the measurement errors.
3. RESULTS
Table 1. Summary of Data
Hα (resolutiona, seeing limit) CO (resolution, beam size)
Perseus CFHT (255 pc, ∼ 1 kpc) N/A
Abell 2597 MUSE (0.3 kpc, ∼ 1.5 kpc) ALMA (0.2 kpc, ∼ 0.9 kpc) Virgo MUSEb(16 pc, ∼ 80 pc) ALMAc
Note. a. This is the pixel size of the velocity maps shown in Figure2. b. MUSE data only covers the central ∼ 4 kpc of Virgo, and does not include the outer filaments. c. ALMA has observed only one molecular complex at a projected distance of 3 kpc from the center of Virgo (Simionescu et al. 2018).
0 20 40 60 80
separation (kpc)
0 1 2 3 4number of pairs
1e5Perseus
0 10 20 30 40separation (kpc)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0number of pairs
1e5Abell 2597
0 2 4 6separation (kpc)
0 1 2 3 4 5number of pairs
1e6Virgo
0 10 20 30 40 50 60velocity error (km/s)
0 50 100 150 200250
Perseus all data
Perseus data used
0 10 20 30 40
velocity error (km/s)
0 50 100 150 200250
Abell 2597 all data
Abell 2597 data used
0 10 20 30 40 50
velocity error (km/s)
0 200 400 600 800 10001200
Virgo all data
Virgo data used
Figure 1. Top left to right: distribution of velocity errors in Perseus, Abell 2597, and Virgo. Bottom left to right: distribution of pair separations. The grey areas denote where the number of pairs drops below 20% of the peak. For Perseus and Abell 2597, the peak scales are ∼ 15 kpc and ∼ 10 kpc, respectively. They roughly correspond to the radius of the regions that contain most of the filaments. In Virgo, the peak scale corresponds to the size of the region observed by MUSE.
To better reveal the driving source of turbulence, we divide the filaments in Perseus into inner (r < 12 kpc) and outer filaments (r > 12 kpc). We choose this divid-ing radius r = 12 kpc such that there are comparable total numbers of pixels in the inner and the outer re-gions. We have verified that the results are not sensitive to the exact value of this radius.
As the top right panel of Figure2shows, the VSF of the inner filaments shows a similar shape as the VSF of all the filaments, but a larger amplitude and a more prominent break at r . 10 kpc. This is roughly the size of the inner X-ray bubbles of Perseus (Fabian et al. 2003), suggesting that the driver of turbulence is AGN
Perseus
12 kpc 300 200 100 0 100 200 300line-of-sight velocity (km/s)
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/s)
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/s)
Abell 2597 All
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Virgo
1 kpc 200 100 0 100 200line-of-sight velocity (km/s)
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Hitomi has measured the line-of-sight velocity disper-sion in the core of Perseus at much lower spatial res-olution (Hitomi Collaboration et al. 2016). Our mea-sured velocities at and above the driving scale for the inner and outer filaments agree with the Hitomi mea-surements of the inner and outer regions (Hitomi Col-laboration et al. 2018) of the Perseus core (Figure3). In addition, the VSF of the outer filaments shows remark-able agreement with that inferred from the analysis of X-ray surface brightness fluctuations of similar regions (Zhuravleva et al. 2014) (see Appendix for detail).
The inner filaments of Abell 2597 reveal a driving scale of ∼ 4 kpc (middle panels of Figure2), which is also seen in the VSF of the molecular gas observed by ALMA. The driving scale is again consistent with the size of the inner X-ray bubbles filled with radio-emitting plasma (Tremblay et al. 2012). For the outer filaments of Abell 2597, the power continues to rise towards larger separa-tions. There is a clear bump between 20 − 30 kpc, which is roughly the distance to the outer X-ray bubbles that are visible on the X-ray map. This feature is also seen in the VSF of the molecular gas. The X-ray observations of Abell 2597 show many shocks, bubbles, and ripples (Tremblay et al. 2012). It is likely that AGN-driven turbulence dominates the entire central region of Abell 2597.
In Virgo (bottom panels of Figure2), we again see a clear connection between AGN feedback and turbulence. The inferred driving scale in the center of Virgo is be-tween 1-2 kpc, which is the size of the bright AGN jet (Marshall et al. 2002) (the linear X-ray feature extend-ing to the right) and also the jet-driven bubble. ALMA has observed a molecular complex located around the lower left corner of the map (Simionescu et al. 2018), and the measured velocity dispersion is in good agree-ment with our results.
For all three clusters, the inferred driving scale is con-sistent with the scenario that AGN feedback is the main driver of turbulence in the centers of galaxy clusters. In addition, the amplitude of the turbulent motion revealed by the VSF is also consistent with this scenario. The largest velocity caused by AGN feedback is roughly the velocity of the post-shock material, which is 32(M − 1)cs
with M being the Mach number of the shock and cs
be-ing the sound speed of the ICM (Li et al. 2017). The measured M in these clusters is ∼ 1.1 − 1.2 ( Trem-blay et al. 2012; Forman et al. 2017), and cs is a few
hundred km/s. Therefore, the post-shock velocities are ∼ 100 − 200 km/s. If turbulence is driven by buoyantly rising bubbles, the largest velocities should be the ve-locities of the bubbles, which are also expected to be a fraction of the sounds speed (Robinson et al. 2004).
10
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1separation (kpc)
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v|
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/s)
Perseus All
inner (r < 12 kpc)
outer (r > 12 kpc)
1/3 (Kolmogorov)
1/2
Chandra 25-40 kpc
Hitomi Region 0
Hitomi Region 3
Figure 3. Comparison with X-ray measurements of the Perseus cluster, including Hitomi (Hitomi Collaboration et al. 2016) X-ray Doppler line broadening measurements (Hitomi Collaboration et al. 2018) and Chandra surface brightness fluctuation analysis (Zhuravleva et al. 2014). The thickness of the lines reflects the uncertainties from mea-surement errors. Because Hitomi measures line broadening along the entire line-of-sight over a rather large projected area (∼ 20 kpc), we cannot derive a VSF from the mea-surements. Thus we show the Hitomi PSF corrected line-of-sight velocity dispersion measurements as horizontal lines with shaded regions reflecting the measurement uncertain-ties. Hitomi Region 0 roughly corresponds to our inner (r < 12 kpc) region, and Hitomi Region 3 covers a large fraction of the outer filaments (corresponding to our r > 12 kpc region) (Hitomi Collaboration et al. 2018). The X-ray surface brightness fluctuation analysis for the r < 40 kpc region excludes r . 25 kpc region due to presence of bub-bles and shocks (see Appendix for more detailed discussions). Thus it roughly corresponds to the outer region of the Hα filaments. Our measured amplitudes of turbulence based on the optical data are in remarkable agreement with the X-ray results.
4. DISCUSSIONS 4.1. The steepening of the VSF
The steepening of the VSF on small scales is puzzling. For all three clusters, the steepening happens on scales well above the seeing limit (see Table1 for a summary of the seeing limit), so it is a real feature (see Section4.2
on small scales, whereas the other two clusters show even steeper slopes, which cannot be explained by supersonic turbulence.
We do not yet have a definitive explanation for the steepening and the exact slopes of the VSFs. There are, however, some interesting theoretical possibilities. On small scales (from near and below the mean free paths down to Larmor radii), gas motion is likely dominated by Alfv´en waves. It is possible that the steepening of the VSF is a result of partial dissipation of certain modes. Magnetic fields can also steepen the kinetic power spec-trum if magnetic tension suppresses the nonlinear decay of g-modes (Bambic et al. 2018a).
Another interesting possibility is that the turbulence cascade is affected by kinetic micro-instabilities, such as firehose and mirror instabilities (Kunz et al. 2014;
Squire et al. 2019). MHD waves, in particular, Alfv´en waves may become unstable to these instabilities (Squire et al. 2017). Turbulent energy in this case would be transferred non-locally from large scales to the much smaller lengths relevant for individual protons, which may result in a steeper spectrum. Future theoretical investigations are required to help understand how these instabilities affect the spectrum of turbulence.
It is also possible that we are seeing features unique to turbulence driven by intermittent AGN feedback. The eddy turnover time associated with scale ` can be esti-mated as t` ∼ `/v`. Our analysis of Perseus reveals a
driving scale L ∼ 10 kpc, and the velocity at the driving scale is vL∼ 140 km/s. Thus tL∼ 70 Myr. The period
of AGN outbursts can be estimated from the inferred age separation of X-ray bubbles (Sanders & Fabian 2007), which gives a period of ∼ 10 Myr, much shorter than tL.
It takes a few tL for turbulence to cascade down from
the driving scale L to the dissipation scale, which means that the time it takes to establish a classic Kolmogorov turbulence is an order of magnitude longer than the in-termittency of the driver. The same is true for Abell 2597 and Virgo.
AGN feedback as a turbulence driver is not only in-termittent (in the sense that it turns on and off on short time-scales compared with tL), its strength,
driv-ing scale and the volume it influences also all change over time. Each outburst grows from small scales to large scales, as does its “sphere of influence”. In this picture, the VSF steepening reflects a suppression of power on small scales, and can be explained by the fact that a fraction of the gas is not as perturbed. The less per-turbed gas may have a Kolmogorov spectrum from the cascade of turbulence driven by structure formation, su-pernova type Ia, and previous AGN activities, but the
amplitude is too low to be detected on scales we are able to probe with confidence here1.
4.2. Limitations and Uncertainties
On small scales, optical observations are affected by “seeing” due to turbulence in the Earth atmosphere. Seeing may have a larger effect on the flux measure-ment, but less on the line-of-sight velocity measurement. The reason is that even though neighboring pixels would share photons due to seeing, the velocity measurement is only sensitive to the shift of the brightest component along the line of sight. If our velocity measurements were strongly affected by seeing, then one would expect a further steepening of the VSF on scales below the see-ing limit. This is not observed in our results as the slope remains the same at the smallest scale measured.
Another source of uncertainties has to do with over-lapping filaments along the line-of-sight. In the central regions, an individual line-of-sight can probe multiple Hα emitting clouds. For all the pixels, we always fit with one Gaussian component. We have individually inspected a large number of pixel fits in Virgo, and ver-ified that in case there are two components along the line-of-sight (which are rare), the fit correctly locks onto the strongest component. Thus even though the veloc-ity dispersion may become large due to overlapping fil-aments (Gendron-Marsolais et al. 2018), the centroid velocity probes only the velocity shift of the brightest filament, and is therefore robust. We also know that the outer filaments do not tend to have this overlapping issue (Conselice et al. 2001). The inner and outer fil-aments show similar VSFs for both Perseus and Abell 2597. This confirms that the overlapping issue does not significantly affect our analysis.
However, we do think that our results can be affected by projection effect. That is, two pixels close to each other in projection may not be physically close to each other, and may show a rather large velocity difference. This affects the VSF on smaller scales more, due to smaller number of pairs and smaller intrinsic velocity differences. Removing the projection effect requires an understanding of the true three-dimensional distribution of the filaments, which we currently do not have. The corrected slope would likely be even steeper than what we show here, but would not change our main conclu-sions.
On large scales, our measurements suffer from the sampling limit. As Figure 1 shows, the total number
10
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Coma X-ray
Figure 4. VSFs with scales normalized by the Kolmogorov microscales. Also shown are the best constraints obtained previously using the X-ray surface brightness fluctuation analysis of the Coma cluster. For comparison, we have also plotted the Perseus X-ray analysis for the r < 40 kpc region (excluding r . 25 kpc). The width of the X-ray curves shows 1σ statistical uncertainties. The dashed grey line shows the prediction from direct numerical simulations (DNS) of hy-drodynamic turbulence with Spitzer viscosity(Ishihara et al. 2016). Our direct detection of turbulence below the Kol-mogorov microscales confirms the previous interpretation of the X-ray surface brightness analysis: the effective viscosity in the ICM is suppressed.
of pairs decreases as the separation gets larger than the size of the whole Hα structure. Thus at large separa-tions, we are only sampling a small fraction of the whole volume, which can cause a bias. The grey areas in the top panels of Figure1denote where the number of pairs drops below 20% of the peak, and the sampling uncer-tainties are considered large. They correspond to the grey areas in Figure2. To better assess the uncertain-ties associated with the sampling limit, we have also examined the distribution of δv at different scales. On scales where we consider sampling uncertainties to be large, the absolute value of the skewness tends to in-crease above ∼ 0.5 − 1. Therefore, we caution against over-interpretation of features in the VSFs on very large scales.
Overall, our results do not appear to be significantly affected by the limitations and uncertainties discussed here. Future optical observations with even better spa-tial and spectral resolutions will help improve the as-sessment of these uncertainties.
4.3. Implications
Our results suggest that the motion of cold filaments is well-coupled with the hot ICM. The origin of the Hα
fila-ments and their fate are still uncertain, but two scenarios would allow the filaments to share the same turbulent motion of the hot ICM: (1) if they originate from the hot gas, either due to thermal instabilities or induced cooling (McCourt et al. 2012; Li & Bryan 2014;Li et al. 2019), but are very short-lived (dissolve quickly) such that they keep the memory of the turbulent motion of the hot gas, and/or (2) if they are very “misty” and quickly become co-moving with the hot gas (McCourt et al. 2018) even if they are created independently of it (Qiu et al. 2019). On the other hand, if the cold gas is poorly coupled to the hot gas and follows ballistic trajectories, neighboring cold filaments would move independently and show lit-tle kinematic correlation. The measured VSF on small scales would be flatter than Kolmogorov, and certainly flatter than what is measured here.
In addition, we can use the turbulent motion of the cold gas to put constraints on microscopic transport pro-cesses in the hot ICM. Figure 4 shows velocities as a function of scales normalized by the Kolmogorov mi-croscales. The Kolmogorov microscale where the turbu-lent kinetic energy is dissipated into heat, and is calcu-lated as η =ν3
1/4
, where ν is the kinematic viscosity and is the energy dissipation rate. The dynamic viscos-ity µ, which is related to the kinetic viscosviscos-ity as µ = ρν, can be estimated as:
µ = 5500 g cm−1s−1 T e 108K 5/2 lnΛ 40 −1 (1) where lnΛ is the Coulomb logarithm (Sarazin 1988). We estimate based on our measured VSF on small scales, which is slightly different from estimated using veloci-ties at the driving scale because the slopes of the VSFs are steeper than Kolmogorov. For gas properties, we use Te = 3 keV and ne = 0.02cm−3 for Perseus (Churazov et al. 2004); for Abell 2597, we use Te = 2.7 keV and
ne = 0.06cm−3 (Tremblay et al. 2012); for Virgo, we
use Te = 1.6 keV and ne = 0.1cm−3 (Zhuravleva et al. 2014).
According to direct numerical simulations (Ishihara et al. 2016), the gas viscosity affects pure hydrody-namic turbulence on scales that are larger than the Kol-mogorov microscale (dashed grey line in Figure4). Our detection of turbulence near and below the Kolmogorov microscale suggests that isotropic viscosity is suppressed in the ICM.
the electron mean free paths in the centers of Perseus and Virgo are ∼ 80 pc and ∼ 8 pc, respectively, about 1/3 − 1/2 the size of our resolution in the two clusters. Figure4also includes the best X-ray constraint on vis-cosity obtained from deep Chandra observations of the Coma cluster (Zhuravleva et al. 2019), where the mean free paths and the Kolmogorov microscales are larger. Our analysis based on the optical data probes the veloc-ity field directly, and shows remarkable agreement with the conclusion of the X-ray surface brightness analysis. Both measurements support suppressed effective viscos-ity in the bulk intergalactic plasma, suggesting that the microphysics of the ICM is driven by magnetic fields operating below the Coulomb mean free path.
4.4. Turbulence as a Heating Source
It has been suggested that the dissipation of turbu-lence can balance radiative cooling in the centers of galaxy clusters based on the analysis of X-ray surface brightness fluctuations (e.g., Zhuravleva et al. 2014). The turbulent heating rate can be estimated as QL ∼
ρv3
L/L with L being the driving scale. Since our
mea-sured VSFs are in excellent agreement with the X-ray analysis within the scales that the X-ray observations probe (near the driving scale), the heating rate is sim-ilar when estimated using turbulence measured at the driving scale.
However, as discussed previously, the slopes of the VSFs studied here tend to be steeper than Kolmogorov turbulence on small scales. If the steepening is caused by suppression of power on small scales, e.g., suppres-sion of the nonlinear decay of gravity waves (Bambic et al. 2018a), or AGN-driven turbulence being nonuni-form, the actual dissipation rate should be somewhat lower than QL. On the other hand, if the steepening is
a result of partial dissipation, the heating rate does not change.
Another concern with AGN-driven turbulence as the main heating mechanism is that it may not propagate far enough to heat up the whole core (Bambic et al. 2018b). However, our VSFs reveal drivers at ∼ 20 kpc in Perseus and Abell 2597, which we interpret as mainly reflecting the motions of the drivers themselves, not the propaga-tions of turbulence from the very center of the cluster. Our analysis shows that turbulence at larger distances from the cluster centers can be generated “in-situ” by rising bubbles and possibly shocks as a result of AGN feedback. Therefore, our result is overall consistent with turbulence as an important heating mechanism.
5. CONCLUSIONS AND FINAL REMARKS
Our study demonstrates the power of high resolution IFU observations in helping us understand the kinemat-ics of multiphase gas. We show that AGN feedback is the main driver of turbulence in the centers of galaxy clusters. The result naturally serves as a test for nu-merical models of AGN feedback. In addition, it also serves as an excellent test for models of cool gas. Our detection of turbulence near the mean free path of the ICM supports suppressed effective viscosity. The slope of the VSF on small scales deviates from the classical Kolmogorov expectation, and points out directions for future theoretical and observational investigations.
ACKNOWLEDGMENTS
We would like to thank Paul Duffell, Peng Oh, Christopher Reynolds, Anna McLeod and Andrea An-toni for helpful discussions. This work was partly per-formed at the Aspen Center for Physics, which is sup-ported by National Science Foundation grant PHY-1607611. We acknowledge the technical support from the Scientific Computing Core of the Simons Founda-tion.
APPENDIX
A. X-RAY ANALYSIS OF FLUCTUATIONS IN THE HOT GAS IN PERSEUS
-0.23 -0.14 -0.065 0.016 0.096 0.18 0.26 0.34 0.42 0.5 0.58 10 kpc
Figure 5. Residual X-ray image of the central r < 40 kpc region in the Perseus cluster used for the surface brightness fluctuation analysis shown in Figure3. The central r . 25 kpc region is excised from the analysis because it is dominated by bubbles and shocks produced by the AGN feedback.
of density fluctuations. Using a statistical linear relation between the power spectrum of density fluctuations and velocity (Zhuravleva et al. 2014;Gaspari et al. 2014), we obtained the power spectrum of gas motions in Perseus.
The innermost r . 25 kpc region is dominated by the prominent structures associated with the bubbles of relativistic plasma and shocks around them (Zhuravleva et al. 2015). Therefore, we carefully select the region where the dynamics of the hot X-ray gas is probed. This region is shown in Figure 5. We effectively use fluctuations in the annulus ∼ 25 − 40 kpc. We additionally check the nature of fluctuations in this region (Ar´evalo et al. 2016;Zhuravleva et al. 2016;Churazov et al. 2016) and confirm that most fluctuations in these regions are of isobaric nature.
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